Refer to the image please!!

Question

asked Nov 5, 2023 197k views

1 Answer

Gambo · Answer 1 · 2023-11-09T18:34:15+0000

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Here we go ~

Value of g (x) is -2, when :

$\qquad \sf  \dashrightarrow \: - 2.5 < x \leqslant - 1.5$

And since -2 lies in this range of x,

$\qquad \sf  \dashrightarrow \:g( - 2) = - 2$

Value of x is -1, when :

$\qquad \sf  \dashrightarrow \: - 1.5 < x \leqslant - 0.5$

And -0.5 falls in this range, hence

$\qquad \sf  \dashrightarrow \:g( - 0.5 ) = - 1$

Next, The value of x is 0 when :

$\qquad \sf  \dashrightarrow \: - 0.5 < x < 0.5$

But, it isnt equal to 0.5, since there is open interval at both extremes.

Next, Value of x is 1, when :

$\qquad \sf  \dashrightarrow \:0.5 \leqslant x < 1.5$

And since it also has the value 0.5 included in it,

$\qquad \sf  \dashrightarrow \:g(0.5) = 1$